Question

Find the volume of the solid generated by revolving about the x-axis by the curve, y2 = 9x and the line y = 3x

Answer 1

$V=2x \int_2^1 (2-x)(x^3+x+1-8)dx$

$=2x\int^2_0(-x^4+2x^3-x^2+2x)dx$

$=[-\frac{x^5}{5}+\frac{x^4}{4}-\frac{x^3}{3}+x^2]_0^1$

$=2\pi[\frac{-1}{5}+\frac{1}{2}+\frac{1}{3}+1]$

$=\frac{29\pi}{15}$